The entry for Aubourn in the National Index of Parish Registers volume on Lincolnshire (published by the Society of Genealogists) includes this note, from the 1851 Religious Census:
Vicar reported in 1851 that two thirds of the people of the village had been Wesleyan Dissenters since 1810.That may be part of the answer, but there's more, this time from GENUKI:
A small Weslyean Methodist chapel was established about 1805 and completely rebuilt in 1845.(See
http://www.genuki.org.uk/big/eng/LIN/Aubourn/#ChurchHistory)
The NIPR doesn't list any marriage registers for the Wesleyan chapel, so it may be that like many other non-conformist places of worship, it wasn't actually authorised for marriages. And some non-Anglicans, it seems, preferred to marry in a register office rather than in the parish church. (And even if Aubourn chapel was authorised for marriages, it's possible that it was out of action around that time while being rebuilt.)
The parish church in Aubourn has an interesting history too, though not strictly relevant here. The original church, dating from abround 1200, was replaced by a much larger one on a different site in 1862. This one, however, was decommissioned in the 1970s, and all that remains is a tall spire, a few walls, and a graveyard; the little old church is once again being used as the parish church. There is a brief account of this on the GENUKI page I referred to, but it implies (incorrectly, I believe) that the later church is still intact. It's the the little old church, with a low spire, that is still standing, and the later one with the tall spire is mostly demolished.
Arthur
